Which is the expression in exponential form?
[tex]$6^{-a}$[/tex]
[tex]$6 a$[/tex]
[tex]$a^{-6}$[/tex]
[tex]$6 a^{-1}$[/tex]
Answer (2)
Identify exponential form as a base raised to a power.
Examine each expression: 6 − a , 6 a , a − 6 , 6 a − 1 .
Determine that 6 − a is in exponential form.
The expression in exponential form is 6 − a .
Explanation
Understanding Exponential Form The question asks us to identify which of the given expressions is in exponential form. An expression is in exponential form if it involves a base raised to a power. Let's examine each option.
Analyzing Each Expression
6 − a : Here, 6 is the base and − a is the exponent. This is in exponential form.
6 a : This represents 6 multiplied by a . This is not in exponential form.
a − 6 : Here, a is the base and − 6 is the exponent. This is in exponential form.
6 a − 1 : This can be written as a 6 . While it contains an exponent, the entire expression is not purely in exponential form.
Identifying the Expression in Exponential Form Both 6 − a and a − 6 fit the definition of exponential form. Since the question does not specify any preference, we can choose either one. Let's choose 6 − a .
Final Answer The expression in exponential form is 6 − a .
Examples
Exponential form is used in various fields, such as calculating compound interest, modeling population growth, and describing radioactive decay. For example, if you invest P dollars at an annual interest rate r compounded n times per year, the amount A you'll have after t years is given by A = P ( 1 + n r ) n t , which is an exponential function. Understanding exponential forms helps in predicting future values based on current conditions.
The expression in exponential form from the given choices is 6 − a . This expression consists of a base (6) raised to an exponent (-a). Both 6 − a and a − 6 qualify as exponential forms, but the selected expression is 6 − a .
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